Status Physics Book:
Observables and Predictions
Convenors:
Elena Bratkovskaya*, Christian Fuchs, Burkhard Kämpfer
*FIAS, J.W. Goethe Universität, Frankfurt am Main
29.05.2006 , CBM Workshop „ The Physics of High Baryon Density „
Content of the Chapter:
Observables and Predictions
based on dynamical models – transport
approaches and hydrodynamics
1. Introduction
2. Excitation function of particle yields
3.
4.
5.
6.
7.
and ratios
Transverse mass spectra
Collective flow
Dileptons
Open and hidden charm
Fluctuations and correlations
Concentrate on FAIR energy range 10-30 A GeV
1. Introduction
FAIR energies are well suited to study
dense and hot nuclear matter –
 a phase transition to QGP ,
 chiral symmetry restoration,
 in-medium effects
(cf. talk by J. Randrup)
Way to study:
Experimental energy scan of different
observables in order to find an ‚anomalous‘
behavior by comparing with theory
2. Excitation function of particle yields and
ratios
AGS NA49
Overview on the experimantal meson and
strange baryon abundancies from central
Au+Au/Pb+Pb collisions versus s 1/2
10
4
10
2
10
0
Multiplicity
Au+Au (central)
10
-2
10
-4
+



__
D(c)
+
K

AGS
SPS
RHIC
HSD ' 99
K
10
J/
D(c)
-6
10
-1
10
0
10
1
10
2
Energy [A GeV]
10
3
10
4
BRAHMS
2. Excitation function of particle yields and ratios
Transport models:
HSD, UrQMD, GiBUU
+
+
K /
y=0
0.25
0.20
0.20
0.15
0.15
E866
NA49
PHENIX
STAR
BRAHMS, 5%
BRAHMS, 10%
0.05
0.00
+
E866
NA49
BRAHMS, 5%
0.05
0.00
0
10
10
1
10
2
10
3
10
4
0.25
10
0
10
1
2
10
10
0.25


0.20
HSD
UrQMD
GiBUU
0.15
3
10


4
<K >/< >
K /
0.20
Ratios
+
<K >/< >
0.10
0.10
Exp. data are not well reproduced
within the hadron-string picture =>
evidence for nonhadronic degrees of
freedom
4
0.25
HSD
UrQMD
0.15
0.10
0.10
0.05
E866
NA49
PHENIX
STAR
BRAHMS, 5%
BRAHMS, 10%
0.00
0
10
10
1
10
2
10
3
10
0.05
0.00
4
0.08
E866
NA49
BRAHMS, 5%
10
0
10
1
2
10
10
3
10
4
0.08
0
<+ >/<>
0
(+ ) / 
0.06
0.06
E877
NA49
STAR
0.04
0.02
E877
NA49
0.04
0.02
0.00
0.00
0
10
10
1
10
2
10
Elab/A [GeV]
3
10
4
10
0
10
1
2
10
10
Elab/A [GeV]
3
10
4
3. Transverse mass spectra
+
Au+Au / Pb+Pb -> K +X
0.35
Transport models:
UrQMD 2.2 (effective heavy resonances with
masses 2 < M < 3 GeV and isotropic decay)
GiBUU
0.30
T [GeV]
• HSD 2.0 (+ Cronin effect)
• UrQMD 2.0
•
0.20
0.15
E866
NA44
BRAHMS
NA49
STAR
PHENIX
0.10
All transport models fail to reproduce the Tslope without introducing special „tricks“
which are, however, inconsistent with other
observables!
10
100

0.35
0.30
T [GeV]
3D-fluid hydrodynamical model
gives the right slope!
Is the matter a parton liquid?
0.25
HSD
HSD with Cronin eff.
UrQMD 2.0,
2.1
GiBUU
3f-hydro
Au+Au / Pb+Pb -> K +X
HSD
HSD with Cronin eff.
UrQMD 2.0,
2.1
3f-hydro
0.25
0.20
0.15
E866
NA44
BRAHMS
NA49
STAR
PHENIX
0.10
10
100
1/2
s
[GeV]
4. Collective flow: general considerations
Y
Non central Au+Au collisions :
interaction between constituents leads to a
pressure gradient => spatial asymmetry is converted
to an asymmetry in momentum space =>
collective flow
v 1 
px  py
2
px  py
2
2
v 2 
- directed flow
px

pT
2

- elliptic flow
V2 > 0 indicates in-plane emission of particles
Out-of-plane
dN
dN
1
1  2v1cos( )  2v 2cos(2 )  ...

dyp Tdp Td dyp Tdp T 2π
Y
In-plane
X
V2 < 0 corresponds to a squeeze-out perpendicular
to the reaction plane (out-of-plane emission)
v2 = 7%, v1=0
v2 = 7%, v1=-7%
v2 = -7%, v1=0
4. Collective flow: v2 excitation function
0.20
0.15
Au+Au, mid-rapidity, semi-central
protons
RBUU (Munich), potential
RBUU (Giessen), potential
RBUU (Giessen), cascade
GiBUU, potential
GBUU, cascade
0.10
v2
0.05
0.00
-0.05
-0.10
-0.15
EOS/ E895/ E877
FOPI/ Plastic Ball/ LAND/ MSU
0.1
1
10
Ebeam [GeV]
 Proton v2 at low energy shows sensitivity to the nucleon potential.
 Cascade codes fail to describe the exp. data.
 AGS energies: transition from squeeze-out to in-plane elliptic flow
4. Collective flow: v2 excitation functions
v2 excitation functions from string-hadronic transport models
– UrQMD:
4. Collective flow: v1 excitation functions
2+1 fluid Hydro
 2+1 fluid Hydro (Frankfurt) predicts
„antiflow“ of protons – if the matter undergoes a
1st order phase transition to the QGP
 Warning: other Hydro models don‘t show such
„antiflow“ => Hydro results are very sensitive to
the initial and „freeze-out“ conditions!
PT – phase transition
MPM – mixed phase EoS
1F,2F,3F –1,2,3 fluid hydro
(Ivanov et al.)
Directed flow v1 & elliptic flow v2 for Pb+Pb at 40 A GeV
Pb+Pb, 40 A GeV
protons
0.2
v2
0.0
-0.1
0.0
-0.1
central
-0.2
central
-0.2
-2
0.2
-1
0
1
2
-2
-1
0
1
2
0.0
v2
v1
0.1
0.0
NA49
HSD
UrQMD
3f-hydro
-0.1
-0.2
-2
-1
0
1
NA49
HSD
UrQMD
3f-hydro
-0.1
semi-central
2
-2
-1
0
1
2
0.2
0.2
Experimentally:
breakdown of v2 at
midrapidity !
0.1
v2
0.1
v1
•Too large elliptic flow v
0.0
 Signature for a first
0.0
-0.1
-0.2
-2
-1
-0.1
peripheral
pT < 2 GeV/c
0
y
1
2
-2
-1
order phase transition ?
peripheral
pT < 2 GeV/c
0
y
1
2
at midrapidity from HSD,
UrQMD and 3-fluid hydro
for all centralities !
0.1
semi-central
1 at
midrapidity not described
by HSD, UrQMD and 3fluid hydro
0.1
0.1
v1
•Small wiggle in v
Pb+Pb, 40 A GeV
protons
0.2
2
4. Collective flow: elliptic flow at 25 A GeV
– predictions for CBM
0.20
Transport models
• HSD
predict similar v2 for charged
particles!
AMPT with string melting shows
much stronger v2 for charges
particles !
AMPT w/o string melting
AMPT with string melting
QGSM (Dubna)
QGSM (Oslo-Tuebingen)
UrQMD
HSD
GiBUU
0.15
0.10
v2
• UrQMD
• GiBUU
• QGSM (v. Dubna;
v. Oslo-Tuebingen)
•AMPT without string melting
Au+Au, 25 A GeV, b=7 fm, |y|<1
0.05
0.00
Charged particles
0.0
0.5
1.0
pT [GeV/c]
1.5
2.0
4. Collective flow: elliptic flow at 25 A GeV
– predictions for CBM
0.15
0.15
Au+Au, 25 A GeV, b=7 fm, |y|<1
v2
Au+Au, 25 A GeV, b=7 fm, |y|<1
0.10
0.10
0.05
0.05

0.00
QGSM: v. Dubna Oslo-Tuebingen

-0.05
-0.05
D-Dbar
HSD
-0.10
0.0
0.15
0.00
p

K
0.5
1.0
1.5
2.0
-0.10
0.0
0.15
0.5


p

K
p

K
1.0
1.5
2.0
Au+Au, 25 A GeV, b=7 fm, |y|<1
Au+Au, 25 A GeV, b=7 fm, |y|<1
0.10
0.05
0.05
v2
0.10
0.00
0.00

p

K
-0.05
UrQMD
-0.10
0.0
0.5
-0.05

p

K
GiBUU

1.0
1.5
2.0
-0.10
0.0
pT [GeV/c]
AMPT with string melting shows v2 similar for all particles !
0.5
1.0
pT [GeV/c]
1.5
2.0
5. Dileptons
Dileptons are an ideal probe for vector meson spectroscopy in
the nuclear medium and for the nuclear dynamics !
•Study of in-medium effects with dilepton experiments:
„Historical“ overview – DLS, SPS (CERES, HELIOS)
 Novel experiments – HADES, NA50, CERES, PHENIX
 Future – CBM
• Excitation function for dilepton yields
• Predictions for CBM (e+e- and m+m-)
• Direct photons as a possible observable for CBM ?!
5. Dileptons
High precision NA60 data allow to distinguish among inmedium models!
Clear evidence for a broadening of the r spectral function!
5. Dileptons
0
160
10
0
HSD' 2000
-1
10
21.5 A TeV
160
21.5 A TeV
50
-1
10
50
20
20
10
-2
10
-2
10
10
5
5
10
-3
10
-4
3
-3
3
-4
2 A GeV
10
2 A GeV
+ -
2 -1
dne e /dM [(GeV/c ) ]
10
10
-5
10
Au+Au, b=2 fm
free meson spectral functions
0.2
0.4
0.6
0.8
2
M [GeV/c ]
-5
10
1.0
1.2
Au+Au, b=2 fm
in-medium meson spectral functions
0.2
0.4
0.6
0.8
1.0
1.2
2
M [GeV/c ]
• Dilepton yield increases with energy due to a higher production of mesons
• r melts at practically all energies; w and  show clear peaks on an approx.
exponential background in mass!
10
2
10
1
HSD
10
10
-1
10
-2
10
-3
10
-4
dN/dM [1/(GeV/c )]
+ -
0
Au+Au, 25 A GeV, 5% central
0.10
 
free
in-medium
0.08
0.06
0.04
0.00
0.2
0.4
0.6
0.8
1.0
0.2
1.2
0.4
2
Au+Au, 25 A GeV, 5% central
ratio=inmedium/free
2
dN/dM [1/(GeV/c )]
10
10
Au+Au->m m +X
25 A GeV, 5% central
-1
-3
1.0
3.0
+ -
-2
0.8
2
0
10
0.6
M [GeV/c ]
M [GeV/c ]
10
free
in-medium
0.02
free
in-medium
0.0
10
 
mm:
ee:
2
Au+Au->e e +X
25 A GeV, 5% central
2
dN/dM [1/(GeV/c )]
5. Dileptons – prediction for CBM
free
in-medium
2.5
+ 
ee
 
2.0
mm
1.5
1.0
0.5
0.0
-4
0.0
0.2
0.4
0.6
0.8
2
M [GeV/c ]
1.0
1.2
0.2
0.4
0.6
0.8
2
M [GeV/c ]
In-medium modifications of e+e- and m+m- spectra are very similar!
1.0
6. Open and hidden charm
Heavy flavor sector reflects the actual dynamics
since heavy hadrons can only be formed in the very
early phase of heavy-ion collisions at FAIR/SPS!
S+U, 200 A GeV
Hidden charm: J/ , ‘
Anomalous J/ suppression in A+A
(NA38/NA50)
Comover dissociation in the transport
approaches – HSD & UrQMD
NA50 data are consistent with
comover absorption models
40
30
20
10
NA38
HSD
0
0
20
40
60
80
100
Pb+Pb, 160 A GeV
50
Bmm(J/)/(DY)|2.9-4.5

Bmm(J/)/(DY)|2.9-4.5
50
NA50 (2000):
anal. A
anal. B
anal. C
40
30
20
HSD
UrQMD
10
0
0
20
40
60
80
ET [GeV]
100
120
140
6. Open and hidden charm
Satz, Digal, Fortuna to (percolation)
Rapp, Grandchamp, Brown (diss. and recomb.)
Capella, Ferreiro (comovers)
New NA60 data for In+In at 160 A GeV: no consistent description has
been found so far with Glauber type comover absorption models
Note: no final transport calculations yet for In+In! (work in progress!)
6. Open and hidden charm
 Open charm: D-mesons
• Dropping D-meson masses with increasing light quark density
might give a large enhancement of the open charm yield at 25 A GeV !
1900
__
D+D
1700
QCD sum rule
1600
Ch. SU(4) model:
MFT
RHA
1500
1400
-4
10
HSD

D
1300
0
-6
1
2
3
bare
in-medium
4
Coupled
channel
1800
10
1700
QCD sum rule

D
1600
+
mD [MeV]
-1
-2
(2mT) dN/dmT [GeV ]
10

Au+Au, 25 A GeV, central
-2
mD [MeV]
1800
-8
10
2.0
2.5
3.0
mT [GeV]
1500
Ch. SU(4) model:
MFT
RHA
3.5
1400
1300
0
1
2
rB/r0
3
4
6. Open and hidden charm
0.020
Bmm(')'/Bmm(J/)J/
S+U, 200 A GeV
0.015
HSD, set 1
HSD, set 2
0.010
0.005
co-mover model
suppression in QGP
0.000
0
20
40
60
80
100
0.020
Bmm(')'/Bmm(J/)J/
Pb+Pb, 160 A GeV
0.015
In-medium reduction of D/Dbar
co-mover model
suppression in QGP
SCM
HSD, set 1
HSD, set 2
0.010
0.005
0.000
0
20
40
60
80
100
120
140
160
masses might have a strong
influence on ‘ suppression due to
the opening of the ‘->D Dbar
decay channel [Rapp, Brown et al.]
ET [GeV]
The ‘/J/ ratio gives information about the approach to chemical
equilibration: charm chemical equilibration is not achieved in HSD
since the ‘ mesons are more suppressed relative to J/
6. Open and hidden charm predictions for CBM
10
5
10
3
10
1
Au+Au, 25 A GeV, central
HSD
-2
(2mT) dN/dmT [GeV ]
Au+Au (central)
0.8
Hidden charm
0.6
0.4
S
-1
HSD
J/
survival factor
1.0
0.2
CBM
0.0
20
40
60
80
100
120
Energy [A GeV]
140
160
10
-1
10
-3
10
-5
Open charm

K

__
10
-7
10
-9
D+D:
J/
0
bare,
1
in-med.
2
3
4
mT [GeV]
Open charm:
without medium effects: suppression of D-meson spectra by factor ~ 10
relative to the global mT-scaling
 with medium effects: restoration of the global mT-scaling for the mesons
Hidden charm:
J/ suppression due to comover absorption at FAIR is lower as at SPS

7. Fluctuations and correlations
Fluctuation and correlation measurements provide
information on susceptibilities of matter: rapid
changes reflect the order of the phase transition
 Multiplicity fluctuations w of negatively, positively and all charged
particles as a function of the number of projectile participants Npartproj :
Var(N)
w

N
N2  N
2
N
w=1 - Poissonian multiplicity
distribution with no
dynamical correlations
HSD and UrQMD show strong multiplicity fluctuations in 4 ‚full‘ acceptance,
however, the observed (by NA49) non-trivial system size dependence of
multiplicity fluctuations is not reproduced by HSD and UrQMD !
7. Fluctuations and correlations
 Predictions: Excitation function of the correlation coefficient C
for
central Pb+Pb and minimum bias p+p collisions calculated within UrQMD:
C BS
1
(n) (n)  1
(n)  1
(n) 
B
S

B
S




  N n 
N n
N n

 3
2
1
(n) 2  1
(n) 
 S   N n S 
N n
 
B(n) , S(n) – baryon number and
strangeness in a given event (n)
 Energy dependence of eventby-event fluctuations of the ratios
(K++K-)/(++-) and
(p+pbar)/(++-) within the
UrQMD model:
BS
Summary
• FAIR is an excellent facility to
study the properties of sQGP
(strongly interacting ‚color liquid‘)
as well as hadronic matter
• Transport theory is the
general basis for an
understanding of nuclear
dynamics on a microscopic level
UrQMD: U+U, 25 A GeV
How to model a phase transition
from hadronic to partonic matter?